The unbounded fractional authoritative camera is a version of the fractional
authoritative camera that can be used with fractions `> 1`.

Most of the reasoning principles for this version of the fractional
authoritative cameras are the same as for the original version. There are two
difference:

- We get the additional rule that can be used to allocate a "surplus", i.e.
  if we have the authoritative element we can always increase its fraction
  and allocate a new fragment.

      ✓ (a ⋅ b) → ●U{p} a ~~> ●U{p + q} (a ⋅ b) ⋅ ◯U{q} b

- At the cost of that, we no longer have the `◯U{1} a` is an exclusive
  fragmental element (cf. `frac_auth_frag_validN_op_1_l`).

We add a specific constructor to the type of expressions for injecting
values in expressions.

The advantage are :
- Values can be assumed to be always closed when performing
  substitutions (even though they could contain free variables, but it
  turns out it does not cause any problem in the proofs in
  practice). This means that we no longer need the `Closed` typeclass
  and everything that comes with it (all the reflection-based machinery
  contained in tactics.v is no longer necessary). I have not measured
  anything, but I guess this would have a significant performance
  impact.

- There is only one constructor for values. As a result, the AsVal and
  IntoVal typeclasses are no longer necessary: an expression which is
  a value will always unify with `Val _`, and therefore lemmas can be
  stated using this constructor.

Of course, this means that there are two ways of writing such a thing
as "The pair of integers 1 and 2": Either by using the value
constructor applied to the pair represented as a value, or by using
the expression pair constructor. So we add reduction rules that
transform reduced pair, injection and closure expressions into values.
At first, this seems weird, because of the redundancy. But in fact,
this has some meaning, since the machine migth actually be doing
something to e.g., allocate the pair or the closure.

These additional steps of computation show up in the proofs, and some
additional wp_* tactics need to be called.

Snapshot will re-appear in iris-examples eventually

Marianna Rapoport authored 6 years ago and Ralf Jung committed 6 years ago

- Removing admitted prophecy spec and making prophecy-related examples (coin-flip and atomic-pair-snapshot) work with the new prophecy support in heap_lang
- Adjusting heap_lang tactics for automation of substitution, closedness, etc. to support prophecy syntax
- Adding notation for prophecy syntax

Marianna Rapoport authored 6 years ago and Ralf Jung committed 6 years ago

- Removing head of list of observations after each reduction step in definition of wp
- Adding support for observations to state_interp and world
- Applying Ralf's suggestions to previous commit (e.g. replacing /\ and -> with unicode characters)

* move PROP-envs definitions to environments.v so that we can control them without pulling in coq_tactics
* use reduction-controlled `pm_default` for proofmode accessors

The BI interface is then instantiated using these laws.  In particular, this
shows that the rules we claim to be admissible actually are.

Fixes #193

New atomic updates: defined as a fixed point with existential quantifier; intro lemma using class of Laterable assertions

move test suite out of theories/ so it does not get installed; also check output of test suite so that we can test printing